Wendy Piatt, the director general of the Russell Group, and the chairman, Professor Michael Arthur, say UK universities could be eclipsed by overseas institutions if the government cuts funding. Photograph: Sarah Lee for the Guardian

The UK's top universities have warned they will need more public funding if they are to continue to compete with institutions around the world.

The Russell Group, which represents 24 of the UK's leading universities, including Oxford and Cambridge, say other nations are pumping millions of pounds into research and higher education. There is a "real danger" that, without support, overseas universities could take over, it says, leaving the UK unable to compete.

In a foreword to a report on the importance of world-class universities, Russell Group chair Professor Michael Arthur and director general Wendy Piatt say it is vital the government does not cut funding. They argue the UK is fortunate to have some of the world's best universities, which are the "jewels in our crown".

"Many countries of a comparable size and world influence would dearly love to possess even a tiny handful of our leading universities," the foreword says. But it adds: "Worryingly for us, right now many of them are doing everything they can to emulate what we already have."

These countries are investing heavily in research and development, concentrating their funding in a "limited number of institutions", it says.

The US and China have invested "substantial sums", while other nations are attempting to build a small number of research-intensive universities. South Korea has invested £1.2bn and Germany has plans to invest £2bn, it adds.

Arthur and Piatt say they fear this approach will "pay dividends".

"Our competitors increasingly recognise they need a more diverse higher education system and that nations can't afford to fund all universities at the same level," it says. They argue the UK needs a range of universities catering to different kinds of students.

The report insists that while the UK's leading universities raise their own funds, they also need the support of "concentrated public funding" if they are to continue to compete globally and contribute in terms of research.

"It's vital that in straitened economic times, the UK government does not make the grave mistake of making cuts to higher education and research funding or spreading limited funds too thinly," the foreword says. "UK government policy has, to some extent, recognised the importance of investing in research, concentrating resources on excellence and allowing universities to raise more funds from private sources.

"But to compete globally our leading institutions must be able to secure sufficient funds. Only that way can they boost our economy and prosper in ways that will benefit everyone."

The warning comes as another report found the government has "badly underestimated" the cost to the public purse of raising university tuition fees to a maximum of £9,000 a year.

The study by the Higher Education Policy Institute (HEPI) says the government's assessment about the net cost of the loans it will give to students to cover their fees (the RAB cost) depends on "highly uncertain and unrealistic assumptions". And the effect of student loans on inflation could lead to a rise in the cost of benefits such as pensions.

"We think the government has badly underestimated what loans will cost them because they have made unrealistic and, in some cases, wrong assumptions," HEPI director Bahram Bekhradnia said.

"One of these is that they have assumed average fees of £7,500. We know that average fees are over £8,200. They haven't changed their assumption."

At the same time, the government has also supposed the salary increases achieved by graduates will be spread out evenly, Bekhradnia said.

But in reality, the report argues that over the last 30 years the evidence shows that the highest earning graduates have seen substantial salary increases, while those earning less see modest increases at most.

This could have an impact on the loan repayments the government receives.

The report says student loans are one of the measures included when calculating inflation.

The Office for Budget Responsibility has said that loans will add 0.2% to inflation the first year that they are introduced.

This increased inflation will lead to "bigger rises in various state benefits and civil service pensions", the report says.

It argues that if this inflationary effect increases year on year, and the government does not take action to prevent it, it could generate additional expenditure for the government of between £420 million and £1.14 billion a year.